Meredith Vieira: Why I'm Leaving the Today Show

After Meredith Vieira announced that she was leaving the Today show last month, tabloids began buzzing that she was planning to spend her days caring for her husband, journalist Richard Cohen, who has multiple sclerosis.

Not so, the TV anchor tells PEOPLE in this week’s issue.

"It was being distorted, because it looked better to make it, 'Poor Meredith, she triumphs through it all,' but that wasn't the case," says Vieira, 57. Her husband, 67, would agree.

His reaction to the rumor? "Richard said, 'What is this? You never tend to me! You won’t even get me a cup of coffee!' " jokes Vieira. "I said, 'I know! This scam is working!' But enough gets to be enough."

Tired of waking up at 2:30 a.m. to tape the NBC morning show, Vieira decided she wanted to spend more time with her husband, whose health has been good recently, and her children, Ben, 22, a recent Stanford graduate, Gabe, 19, and Lily, 18, who is about to leave for college.

"We don't know from day to day what might happen," she says. "So why not enjoy life now? It's very precious, and anyone living with any kind of illness knows that. Health is fleeting, and you need to celebrate it while you still have it."

For more on Vieira's decision to walk away from her reported $10 million salary – and all the details of her final show on June 8 – pick up the new issue of PEOPLE, on newsstands Friday